Chamberlain was hurt while playing with his son Thursday at a local spot that had trampoline and related type of equipment.
"I know he did it on the trampoline, that he was bouncing," Girardi said on Saturday.
Yankees general manager Brian Cashman visited Chamberlain in the hospital and said the 26-year-old pitcher told him he could be released from the medical facility this weekend.
"If he gets out today or tomorrow, that would be extremely positive," Cashman said.
Chamberlain also told Cashman he could be back on a mound by July. Cashman did not have the results Saturday morning on Chamberlain's MRI exam and CT scan, which were done on Friday.
"That's what he told me the doctors are telling him," Cashman said. "We'll see. I don't know. I'm just passing on what he said, and hopefully that's all accurate. That's the optimistic side. I don't think anybody can tell anybody directly right now anything on that."
There is no official timetable for Chamberlain's return.
"As we know, this is going to be awhile," Girardi said. "We're going to be there for this kid. We're going to get him through it."
Bone broke through the skin during the dislocation.
"When you have an injury like that, the initial concern is (the possibility of an) infection," Girardi said.
Chamberlain had surgery Thursday night. The 6-foot-2, 240-pound righty was working his way back from elbow ligament replacement surgery and was expected to return in June.
Chamberlain's son was not hurt. The boy began kindergarten last year and Chamberlain often tweets about how proud he is of his son's hockey interest.
Cashman hasn't thought about whether Chamberlain's injury was an unacceptable off-field situation.
"He's dealing with so much different stuff, that's certainly not something I'm focused on at this point," Cashman said. "I'm sad about it. Anybody who's a father has taken their child to one of these type facilities. It's just a tragic accident. It's a freak accident that has occurred. He was being a father."
In January, Chamberlain agreed to a one-year contract for $1,675,000, up from $1.4 million last year. The deal was not guaranteed.
Chamberlain went 2-0 with a 2.83 ERA in 27 relief appearances last season before elbow surgery June 16.